LMFDB - Embedded newform 414.3.k.a.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,3,Mod(35,414)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 20]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("414.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	414.k (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.2806829445$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			71.1
Character	$\chi$	$=$	414.71
Dual form			414.3.k.a.35.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-1.90263 + 6.47977i) q^{5} +(-7.74127 + 8.93390i) q^{7} +(2.79964 + 0.402527i) q^{8} +O(q^{10})$	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-1.90263 + 6.47977i) q^{5} +(-7.74127 + 8.93390i) q^{7} +(2.79964 + 0.402527i) q^{8} +(-6.25434 - 7.21790i) q^{10} +(-1.39544 - 2.17135i) q^{11} +(-15.9554 - 18.4135i) q^{13} +(-4.70994 - 16.0406i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(17.1606 + 7.83698i) q^{17} +(5.09911 + 11.1655i) q^{19} +(13.3692 - 1.92220i) q^{20} +3.65021 q^{22} +(21.7442 - 7.49613i) q^{23} +(-17.3361 - 11.1412i) q^{25} +(34.1059 - 4.90369i) q^{26} +(22.6848 + 6.66086i) q^{28} +(-24.1659 - 11.0362i) q^{29} +(5.15642 - 35.8637i) q^{31} +(-1.59372 - 5.42771i) q^{32} +(-22.4444 + 14.4242i) q^{34} +(-43.1608 - 67.1596i) q^{35} +(-44.6329 + 13.1054i) q^{37} +(-17.1824 - 2.47046i) q^{38} +(-7.93497 + 17.3751i) q^{40} +(-4.50009 + 15.3259i) q^{41} +(-0.512794 - 3.56656i) q^{43} +(-2.79088 + 4.34270i) q^{44} +(-7.70694 + 31.6007i) q^{46} -79.2879i q^{47} +(-12.9139 - 89.8183i) q^{49} +(26.5097 - 12.1066i) q^{50} +(-20.2428 + 44.3254i) q^{52} +(49.7226 + 43.0849i) q^{53} +(16.7249 - 4.91086i) q^{55} +(-25.2689 + 21.8956i) q^{56} +(31.6067 - 20.3124i) q^{58} +(-38.0838 + 32.9998i) q^{59} +(0.442839 - 3.08002i) q^{61} +(38.7249 + 33.5554i) q^{62} +(7.67594 + 2.25386i) q^{64} +(149.672 - 68.3530i) q^{65} +(-59.6258 - 38.3192i) q^{67} -37.7309i q^{68} +112.901 q^{70} +(-55.4188 + 86.2333i) q^{71} +(0.255877 + 0.560292i) q^{73} +(18.5338 - 63.1204i) q^{74} +(16.0765 - 18.5533i) q^{76} +(30.2011 + 4.34227i) q^{77} +(-89.4179 - 103.194i) q^{79} +(-14.6045 - 22.7250i) q^{80} +(-14.7927 - 17.0717i) q^{82} +(-8.41661 - 28.6644i) q^{83} +(-83.4322 + 96.2858i) q^{85} +(4.63525 + 2.11685i) q^{86} +(-3.03270 - 6.64070i) q^{88} +(-139.890 + 20.1131i) q^{89} +288.019 q^{91} +(-31.7031 - 33.3303i) q^{92} +(94.3298 + 60.6221i) q^{94} +(-82.0516 + 11.7972i) q^{95} +(162.707 + 47.7750i) q^{97} +(116.732 + 53.3095i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^4 - 16 * q^7	$ 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) $ 80 * q + 16 * q^4 - 16 * q^7 + 8 * q^10 + 8 * q^13 - 32 * q^16 - 128 * q^19 - 32 * q^22 - 352 * q^25 + 32 * q^28 + 32 * q^31 - 300 * q^34 - 384 * q^37 - 16 * q^40 + 540 * q^43 - 80 * q^49 - 16 * q^52 + 1244 * q^55 + 424 * q^58 + 568 * q^61 + 64 * q^64 + 60 * q^67 + 296 * q^70 + 36 * q^73 - 96 * q^76 - 1476 * q^79 + 12 * q^82 - 276 * q^85 - 112 * q^88 - 368 * q^91 - 304 * q^94 + 712 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{1}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.764582	+	1.18971i	−0.382291	+	0.594856i
$2$	−0.764582	+	1.18971i	−0.382291	+	0.594856i
$3$		0			0
$3$		0			0
$4$	−0.830830	−	1.81926i	−0.207708	−	0.454816i
$5$	−1.90263	+	6.47977i	−0.380526	+	1.29595i	0.517375	+	0.855759i	$0.326909\pi$
$5$	−1.90263	+	6.47977i	−0.380526	+	1.29595i	−0.897902	+	0.440196i	$0.854909\pi$
$6$		0			0
$7$	−7.74127	+	8.93390i	−1.10590	+	1.27627i	−0.148053	+	0.988979i	$0.547301\pi$
$7$	−7.74127	+	8.93390i	−1.10590	+	1.27627i	−0.957843	+	0.287292i	$0.907245\pi$
$8$	2.79964	+	0.402527i	0.349955	+	0.0503159i
$9$		0			0
$10$	−6.25434	−	7.21790i	−0.625434	−	0.721790i
$11$	−1.39544	−	2.17135i	−0.126858	−	0.197395i	0.772015	−	0.635605i	$-0.219249\pi$
$11$	−1.39544	−	2.17135i	−0.126858	−	0.197395i	−0.898873	+	0.438209i	$0.855613\pi$
$12$		0			0
$13$	−15.9554	−	18.4135i	−1.22733	−	1.41642i	−0.877478	−	0.479616i	$-0.840776\pi$
$13$	−15.9554	−	18.4135i	−1.22733	−	1.41642i	−0.349856	−	0.936803i	$-0.613770\pi$
$14$	−4.70994	−	16.0406i	−0.336424	−	1.14576i
$15$		0			0
$16$	−2.61944	+	3.02300i	−0.163715	+	0.188937i
$17$	17.1606	+	7.83698i	1.00945	+	0.460999i	0.850324	−	0.526260i	$-0.176406\pi$
$17$	17.1606	+	7.83698i	1.00945	+	0.460999i	0.159123	+	0.987259i	$0.449133\pi$
$18$		0			0
$19$	5.09911	+	11.1655i	0.268374	+	0.587658i	0.995056	−	0.0993168i	$-0.0316657\pi$
$19$	5.09911	+	11.1655i	0.268374	+	0.587658i	−0.726682	+	0.686974i	$0.758938\pi$
$20$	13.3692	−	1.92220i	0.668459	−	0.0961099i
$21$		0			0
$22$	3.65021			0.165919
$23$	21.7442	−	7.49613i	0.945398	−	0.325919i
$23$	21.7442	−	7.49613i	0.945398	−	0.325919i
$24$		0			0
$25$	−17.3361	−	11.1412i	−0.693443	−	0.445649i
$26$	34.1059	−	4.90369i	1.31176	−	0.188603i
$27$		0			0
$28$	22.6848	+	6.66086i	0.810172	+	0.237888i
$29$	−24.1659	−	11.0362i	−0.833306	−	0.380558i	−0.0473784	−	0.998877i	$-0.515087\pi$
$29$	−24.1659	−	11.0362i	−0.833306	−	0.380558i	−0.785927	+	0.618319i	$0.787814\pi$
$30$		0			0
$31$	5.15642	−	35.8637i	0.166336	−	1.15689i	−0.720042	−	0.693931i	$-0.755877\pi$
$31$	5.15642	−	35.8637i	0.166336	−	1.15689i	0.886378	−	0.462962i	$-0.153213\pi$
$32$	−1.59372	−	5.42771i	−0.0498038	−	0.169616i
$33$		0			0
$34$	−22.4444	+	14.4242i	−0.660130	+	0.424240i
$35$	−43.1608	−	67.1596i	−1.23317	−	1.91885i
$36$		0			0
$37$	−44.6329	+	13.1054i	−1.20629	+	0.354200i	−0.822256	−	0.569118i	$-0.807285\pi$
$37$	−44.6329	+	13.1054i	−1.20629	+	0.354200i	−0.384038	+	0.923317i	$0.625467\pi$
$38$	−17.1824	−	2.47046i	−0.452169	−	0.0650120i
$39$		0			0
$40$	−7.93497	+	17.3751i	−0.198374	+	0.434379i
$41$	−4.50009	+	15.3259i	−0.109758	+	0.373802i	−0.995993	−	0.0894347i	$-0.971494\pi$
$41$	−4.50009	+	15.3259i	−0.109758	+	0.373802i	0.886234	+	0.463237i	$0.153312\pi$
$42$		0			0
$43$	−0.512794	−	3.56656i	−0.0119254	−	0.0829432i	0.982990	−	0.183661i	$-0.0587950\pi$
$43$	−0.512794	−	3.56656i	−0.0119254	−	0.0829432i	−0.994915	+	0.100718i	$0.967886\pi$
$44$	−2.79088	+	4.34270i	−0.0634292	+	0.0986977i
$45$		0			0
$46$	−7.70694	+	31.6007i	−0.167542	+	0.686971i
$47$		−	79.2879i		−	1.68698i	−0.537147	−	0.843489i	$-0.680498\pi$
$47$		−	79.2879i		−	1.68698i	0.537147	−	0.843489i	$-0.319502\pi$
$48$		0			0
$49$	−12.9139	−	89.8183i	−0.263549	−	1.83303i
$50$	26.5097	−	12.1066i	0.530194	−	0.242131i
$51$		0			0
$52$	−20.2428	+	44.3254i	−0.389284	+	0.852412i
$53$	49.7226	+	43.0849i	0.938162	+	0.812922i	0.982532	−	0.186093i	$-0.0595826\pi$
$53$	49.7226	+	43.0849i	0.938162	+	0.812922i	−0.0443699	+	0.999015i	$0.514128\pi$
$54$		0			0
$55$	16.7249	−	4.91086i	0.304088	−	0.0892884i
$56$	−25.2689	+	21.8956i	−0.451230	+	0.390993i
$57$		0			0
$58$	31.6067	−	20.3124i	0.544942	−	0.350213i
$59$	−38.0838	+	32.9998i	−0.645489	+	0.559319i	−0.914887	−	0.403710i	$-0.867721\pi$
$59$	−38.0838	+	32.9998i	−0.645489	+	0.559319i	0.269398	+	0.963029i	$0.413175\pi$
$60$		0			0
$61$	0.442839	−	3.08002i	0.00725966	−	0.0504921i	−0.985870	−	0.167515i	$-0.946426\pi$
$61$	0.442839	−	3.08002i	0.00725966	−	0.0504921i	0.993129	+	0.117023i	$0.0373350\pi$
$62$	38.7249	+	33.5554i	0.624596	+	0.541215i
$63$		0			0
$64$	7.67594	+	2.25386i	0.119937	+	0.0352166i
$65$	149.672	−	68.3530i	2.30265	−	1.05158i
$66$		0			0
$67$	−59.6258	−	38.3192i	−0.889938	−	0.571928i	0.0138524	−	0.999904i	$-0.495590\pi$
$67$	−59.6258	−	38.3192i	−0.889938	−	0.571928i	−0.903790	+	0.427976i	$0.859227\pi$
$68$		−	37.7309i		−	0.554866i
$69$		0			0
$70$	112.901			1.61287
$71$	−55.4188	+	86.2333i	−0.780546	+	1.21455i	0.191898	+	0.981415i	$0.438536\pi$
$71$	−55.4188	+	86.2333i	−0.780546	+	1.21455i	−0.972444	+	0.233138i	$0.925101\pi$
$72$		0			0
$73$	0.255877	+	0.560292i	0.00350516	+	0.00767523i	0.911376	−	0.411574i	$-0.135021\pi$
$73$	0.255877	+	0.560292i	0.00350516	+	0.00767523i	−0.907871	+	0.419249i	$0.862293\pi$
$74$	18.5338	−	63.1204i	0.250457	−	0.852979i
$75$		0			0
$76$	16.0765	−	18.5533i	0.211533	−	0.244122i
$77$	30.2011	+	4.34227i	0.392222	+	0.0563931i
$78$		0			0
$79$	−89.4179	−	103.194i	−1.13187	−	1.30625i	−0.946179	−	0.323642i	$-0.895093\pi$
$79$	−89.4179	−	103.194i	−1.13187	−	1.30625i	−0.185693	−	0.982608i	$-0.559453\pi$
$80$	−14.6045	−	22.7250i	−0.182556	−	0.284063i
$81$		0			0
$82$	−14.7927	−	17.0717i	−0.180399	−	0.208192i
$83$	−8.41661	−	28.6644i	−0.101405	−	0.345354i	0.893125	−	0.449809i	$-0.148508\pi$
$83$	−8.41661	−	28.6644i	−0.101405	−	0.345354i	−0.994530	+	0.104456i	$0.966690\pi$
$84$		0			0
$85$	−83.4322	+	96.2858i	−0.981555	+	1.13277i
$86$	4.63525	+	2.11685i	0.0538983	+	0.0246145i
$87$		0			0
$88$	−3.03270	−	6.64070i	−0.0344626	−	0.0754625i
$89$	−139.890	+	20.1131i	−1.57180	+	0.225990i	−0.872418	−	0.488760i	$-0.837449\pi$
$89$	−139.890	+	20.1131i	−1.57180	+	0.225990i	−0.699379	+	0.714751i	$0.746540\pi$
$90$		0			0
$91$	288.019			3.16504
$92$	−31.7031	−	33.3303i	−0.344599	−	0.362286i
$93$		0			0
$94$	94.3298	+	60.6221i	1.00351	+	0.644916i
$95$	−82.0516	+	11.7972i	−0.863701	+	0.124181i
$96$		0			0
$97$	162.707	+	47.7750i	1.67739	+	0.492525i	0.975544	−	0.219805i	$-0.0705422\pi$
$97$	162.707	+	47.7750i	1.67739	+	0.492525i	0.701844	+	0.712331i	$0.252360\pi$
$98$	116.732	+	53.3095i	1.19114	+	0.543975i
$99$		0			0
$100$	−5.86549	+	40.7954i	−0.0586549	+	0.407954i
$101$	8.40929	+	28.6394i	0.0832603	+	0.283558i	0.990590	−	0.136861i	$-0.0437012\pi$
$101$	8.40929	+	28.6394i	0.0832603	+	0.283558i	−0.907330	+	0.420419i	$0.861883\pi$
$102$		0			0
$103$	−47.2928	+	30.3933i	−0.459154	+	0.295080i	−0.749696	−	0.661782i	$-0.769801\pi$
$103$	−47.2928	+	30.3933i	−0.459154	+	0.295080i	0.290543	+	0.956862i	$0.406164\pi$
$104$	−37.2573	−	57.9735i	−0.358243	−	0.557437i
$105$		0			0
$106$	−89.2756	+	26.2137i	−0.842223	+	0.247299i
$107$	12.6115	+	1.81327i	0.117865	+	0.0169464i	0.200995	−	0.979592i	$-0.435583\pi$
$107$	12.6115	+	1.81327i	0.117865	+	0.0169464i	−0.0831299	+	0.996539i	$0.526492\pi$
$108$		0			0
$109$	−37.3163	+	81.7113i	−0.342351	+	0.749645i	−0.999993	−	0.00368599i	$-0.998827\pi$
$109$	−37.3163	+	81.7113i	−0.342351	+	0.749645i	0.657642	+	0.753331i	$0.271554\pi$
$110$	−6.94501	+	23.6525i	−0.0631364	+	0.215023i
$111$		0			0
$112$	−6.72936	−	46.8037i	−0.0600835	−	0.417890i
$113$	−37.7071	+	58.6734i	−0.333691	+	0.519233i	−0.967037	−	0.254635i	$-0.918045\pi$
$113$	−37.7071	+	58.6734i	−0.333691	+	0.519233i	0.633346	+	0.773869i	$0.281681\pi$
$114$		0			0
$115$	7.20206	+	155.159i	0.0626266	+	1.34921i
$116$			53.1333i			0.458045i
$117$		0			0
$118$	−10.1421	−	70.5399i	−0.0859500	−	0.597796i
$119$	−202.860	+	92.6429i	−1.70470	+	0.778512i
$120$		0			0
$121$	47.4977	−	104.005i	0.392543	−	0.859549i
$122$	3.32575	+	2.88177i	0.0272602	+	0.0236211i
$123$		0			0
$124$	−69.5296	+	20.4157i	−0.560723	+	0.164643i
$125$	−22.4189	+	19.4261i	−0.179351	+	0.155408i
$126$		0			0
$127$	102.639	−	65.9622i	0.808183	−	0.519388i	−0.0700938	−	0.997540i	$-0.522330\pi$
$127$	102.639	−	65.9622i	0.808183	−	0.519388i	0.878277	+	0.478153i	$0.158693\pi$
$128$	−8.55033	+	7.40890i	−0.0667995	+	0.0578821i
$129$		0			0
$130$	−33.1162	+	230.328i	−0.254740	+	1.77176i
$131$	6.58012	+	5.70170i	0.0502299	+	0.0435244i	0.679614	−	0.733570i	$-0.262147\pi$
$131$	6.58012	+	5.70170i	0.0502299	+	0.0435244i	−0.629384	+	0.777094i	$0.716693\pi$
$132$		0			0
$133$	−139.225	−	40.8802i	−1.04680	−	0.307370i
$134$	91.1776	−	41.6394i	0.680430	−	0.310742i
$135$		0			0
$136$	44.8889	+	28.8483i	0.330065	+	0.212120i
$137$			216.729i			1.58196i	0.611842	+	0.790980i	$0.290429\pi$
$137$			216.729i			1.58196i	−0.611842	+	0.790980i	$0.709571\pi$
$138$		0			0
$139$	−202.996			−1.46041			−0.730203	−	0.683230i	$-0.760575\pi$
$139$	−202.996			−1.46041			−0.730203	+	0.683230i	$0.760575\pi$
$140$	−86.3217	+	134.319i	−0.616584	+	0.959423i
$141$		0			0
$142$	−60.2206	−	131.865i	−0.424089	−	0.928625i
$143$	−17.7173	+	60.3396i	−0.123897	+	0.421955i
$144$		0			0
$145$	117.491	−	135.591i	0.810280	−	0.935113i
$146$	−0.862225	−	0.123969i	−0.00590565	−	0.000849104i
$147$		0			0
$148$	60.9245	+	70.3106i	0.411652	+	0.475072i
$149$	−47.7552	−	74.3085i	−0.320505	−	0.498715i	0.643195	−	0.765702i	$-0.277608\pi$
$149$	−47.7552	−	74.3085i	−0.320505	−	0.498715i	−0.963700	+	0.266987i	$0.913972\pi$
$150$		0			0
$151$	−166.377	−	192.009i	−1.10183	−	1.27158i	−0.959483	−	0.281765i	$-0.909080\pi$
$151$	−166.377	−	192.009i	−1.10183	−	1.27158i	−0.142348	−	0.989817i	$-0.545465\pi$
$152$	9.78125	+	33.3119i	0.0643503	+	0.219157i
$153$		0			0
$154$	−28.2573	+	32.6106i	−0.183489	+	0.211757i
$155$	222.578	+	101.648i	1.43598	+	0.655792i
$156$		0			0
$157$	48.4486	+	106.088i	0.308590	+	0.675718i	0.998855	−	0.0478388i	$-0.0152334\pi$
$157$	48.4486	+	106.088i	0.308590	+	0.675718i	−0.690265	+	0.723557i	$0.742506\pi$
$158$	191.138	−	27.4815i	1.20974	−	0.173934i
$159$		0			0
$160$	38.2026			0.238766
$161$	−101.358	+	252.290i	−0.629551	+	1.56702i
$162$		0			0
$163$	−87.5780	−	56.2830i	−0.537289	−	0.345294i	0.243689	−	0.969853i	$-0.421642\pi$
$163$	−87.5780	−	56.2830i	−0.537289	−	0.345294i	−0.780978	+	0.624559i	$0.785279\pi$
$164$	31.6207	−	4.54636i	0.192809	−	0.0277217i
$165$		0			0
$166$	40.5375	+	11.9029i	0.244202	+	0.0717041i
$167$	2.25698	+	1.03073i	0.0135148	+	0.00617202i	0.422161	−	0.906521i	$-0.361272\pi$
$167$	2.25698	+	1.03073i	0.0135148	+	0.00617202i	−0.408646	+	0.912693i	$0.633999\pi$
$168$		0			0
$169$	−60.4310	+	420.307i	−0.357580	+	2.48702i
$170$	−50.7617	−	172.879i	−0.298598	−	1.01693i
$171$		0			0
$172$	−6.06247	+	3.89611i	−0.0352469	+	0.0226518i
$173$	12.0949	+	18.8200i	0.0699125	+	0.108786i	0.874449	−	0.485117i	$-0.161223\pi$
$173$	12.0949	+	18.8200i	0.0699125	+	0.108786i	−0.804537	+	0.593903i	$0.797586\pi$
$174$		0			0
$175$	233.738	−	68.6316i	1.33564	−	0.392181i
$176$	10.2193	+	1.46931i	0.0580640	+	0.00834835i
$177$		0			0
$178$	83.0284	−	181.807i	0.466452	−	1.02139i
$179$	−2.21870	+	7.55620i	−0.0123950	+	0.0422134i	−0.965458	−	0.260558i	$-0.916094\pi$
$179$	−2.21870	+	7.55620i	−0.0123950	+	0.0422134i	0.953063	+	0.302771i	$0.0979118\pi$
$180$		0			0
$181$	−1.82235	−	12.6748i	−0.0100683	−	0.0700262i	0.984168	−	0.177239i	$-0.0567165\pi$
$181$	−1.82235	−	12.6748i	−0.0100683	−	0.0700262i	−0.994236	+	0.107213i	$0.965807\pi$
$182$	−220.214	+	342.659i	−1.20997	+	1.88274i
$183$		0			0
$184$	63.8931	−	12.2338i	0.347245	−	0.0664882i
$185$		−	314.146i		−	1.69808i
$186$		0			0
$187$	−6.92978	−	48.1977i	−0.0370577	−	0.257742i
$188$	−144.246	+	65.8748i	−0.767264	+	0.350398i
$189$		0			0
$190$	48.6998	−	106.638i	0.256315	−	0.561251i
$191$	−25.2390	−	21.8697i	−0.132141	−	0.114501i	0.586283	−	0.810107i	$-0.300591\pi$
$191$	−25.2390	−	21.8697i	−0.132141	−	0.114501i	−0.718424	+	0.695605i	$0.755136\pi$
$192$		0			0
$193$	168.384	−	49.4420i	0.872456	−	0.256176i	0.185296	−	0.982683i	$-0.440675\pi$
$193$	168.384	−	49.4420i	0.872456	−	0.256176i	0.687160	+	0.726506i	$0.258857\pi$
$194$	−181.241	+	157.046i	−0.934232	+	0.809516i
$195$		0			0
$196$	−152.674	+	98.1175i	−0.778948	+	0.500600i
$197$	20.0241	−	17.3510i	0.101645	−	0.0880760i	−0.602556	−	0.798077i	$-0.705851\pi$
$197$	20.0241	−	17.3510i	0.101645	−	0.0880760i	0.704201	+	0.710001i	$0.251305\pi$
$198$		0			0
$199$	−6.93905	+	48.2622i	−0.0348696	+	0.242524i	−0.999800	−	0.0199811i	$-0.993639\pi$
$199$	−6.93905	+	48.2622i	−0.0348696	+	0.242524i	0.964931	+	0.262505i	$0.0845485\pi$
$200$	−44.0501	−	38.1696i	−0.220251	−	0.190848i
$201$		0			0
$202$	−40.5022	−	11.8925i	−0.200506	−	0.0588739i
$203$	285.671	−	130.461i	1.40724	−	0.642667i
$204$		0			0
$205$	−90.7463	−	58.3191i	−0.442665	−	0.284483i
$206$		−	79.5030i		−	0.385937i
$207$		0			0
$208$	97.4580			0.468548
$209$	17.1287	−	26.6528i	0.0819554	−	0.127525i
$210$		0			0
$211$	128.416	+	281.193i	0.608609	+	1.33267i	0.923522	+	0.383546i	$0.125297\pi$
$211$	128.416	+	281.193i	0.608609	+	1.33267i	−0.314913	+	0.949121i	$0.601975\pi$
$212$	37.0717	−	126.255i	0.174867	−	0.595541i
$213$		0			0
$214$	−11.7998	+	13.6177i	−0.0551393	+	0.0636342i
$215$	24.0861	+	3.46306i	0.112029	+	0.0161073i
$216$		0			0
$217$	280.485	+	323.697i	1.29256	+	1.49169i
$218$	−68.6815	−	106.871i	−0.315053	−	0.490232i
$219$		0			0
$220$	−22.8297	−	26.3468i	−0.103771	−	0.119758i
$221$	−129.497	−	441.028i	−0.585961	−	1.99560i
$222$		0			0
$223$	66.4635	−	76.7030i	0.298043	−	0.343960i	−0.586900	−	0.809659i	$-0.699652\pi$
$223$	66.4635	−	76.7030i	0.298043	−	0.343960i	0.884943	+	0.465700i	$0.154197\pi$
$224$	60.8281	+	27.7792i	0.271554	+	0.124014i
$225$		0			0
$226$	−40.9743	−	89.7212i	−0.181302	−	0.396996i
$227$	−141.483	+	20.3422i	−0.623273	+	0.0896132i	−0.446714	−	0.894677i	$-0.647406\pi$
$227$	−141.483	+	20.3422i	−0.623273	+	0.0896132i	−0.176559	+	0.984290i	$0.556497\pi$
$228$		0			0
$229$	−386.344			−1.68709			−0.843545	−	0.537059i	$-0.819535\pi$
$229$	−386.344			−1.68709			−0.843545	+	0.537059i	$0.819535\pi$
$230$	−190.102	−	110.064i	−0.826529	−	0.478538i
$231$		0			0
$232$	−63.2133	−	40.6247i	−0.272471	−	0.175107i
$233$	401.670	−	57.7515i	1.72391	−	0.247860i	0.791991	−	0.610533i	$-0.209045\pi$
$233$	401.670	−	57.7515i	1.72391	−	0.247860i	0.931917	+	0.362673i	$0.118136\pi$
$234$		0			0
$235$	513.768	+	150.856i	2.18624	+	0.641939i
$236$	91.6766	+	41.8673i	0.388460	+	0.177404i
$237$		0			0
$238$	44.8844	−	312.178i	0.188590	−	1.31167i
$239$	−22.8024	−	77.6577i	−0.0954074	−	0.324928i	0.897935	−	0.440128i	$-0.145067\pi$
$239$	−22.8024	−	77.6577i	−0.0954074	−	0.324928i	−0.993342	+	0.115201i	$0.963249\pi$
$240$		0			0
$241$	−218.000	+	140.100i	−0.904563	+	0.581327i	−0.908140	−	0.418667i	$-0.862498\pi$
$241$	−218.000	+	140.100i	−0.904563	+	0.581327i	0.00357745	+	0.999994i	$0.498861\pi$
$242$	87.4207	+	136.029i	0.361243	+	0.562104i
$243$		0			0
$244$	−5.97129	+	1.75333i	−0.0244725	+	0.00718577i
$245$	606.572	+	87.2119i	2.47580	+	0.355967i
$246$		0			0
$247$	124.237	−	272.042i	0.502985	−	1.10138i
$248$	28.8722	−	98.3297i	0.116420	−	0.396491i
$249$		0			0
$250$	−5.97037	−	41.5248i	−0.0238815	−	0.166099i
$251$	186.120	−	289.608i	0.741513	−	1.15382i	−0.241521	−	0.970396i	$-0.577646\pi$
$251$	186.120	−	289.608i	0.741513	−	1.15382i	0.983034	−	0.183421i	$-0.0587173\pi$
$252$		0			0
$253$	−46.6194	−	36.7537i	−0.184266	−	0.145272i
$254$			172.545i			0.679310i
$255$		0			0
$256$	−2.27704	−	15.8371i	−0.00889468	−	0.0618638i
$257$	−371.171	+	169.508i	−1.44424	+	0.659564i	−0.974735	−	0.223363i	$-0.928296\pi$
$257$	−371.171	+	169.508i	−1.44424	+	0.659564i	−0.469509	+	0.882928i	$0.655569\pi$
$258$		0			0
$259$	228.433	−	500.198i	0.881980	−	1.93127i
$260$	−248.704	−	215.503i	−0.956555	−	0.828859i
$261$		0			0
$262$	−11.8144	+	3.46903i	−0.0450932	+	0.0132406i
$263$	129.497	−	112.210i	0.492384	−	0.426653i	−0.372948	−	0.927852i	$-0.621653\pi$
$263$	129.497	−	112.210i	0.492384	−	0.426653i	0.865332	+	0.501199i	$0.167108\pi$
$264$		0			0
$265$	−373.784	+	240.216i	−1.41051	+	0.906477i
$266$	155.085	−	134.382i	0.583025	−	0.505194i
$267$		0			0
$268$	−20.1738	+	140.312i	−0.0752754	+	0.523552i
$269$	31.4702	+	27.2691i	0.116990	+	0.101372i	0.711391	−	0.702796i	$-0.248065\pi$
$269$	31.4702	+	27.2691i	0.116990	+	0.101372i	−0.594401	+	0.804169i	$0.702611\pi$
$270$		0			0
$271$	−346.619	−	101.777i	−1.27904	−	0.375559i	−0.429490	−	0.903071i	$-0.641307\pi$
$271$	−346.619	−	101.777i	−1.27904	−	0.375559i	−0.849548	+	0.527512i	$0.823125\pi$
$272$	−68.6424	+	31.3479i	−0.252362	+	0.115250i
$273$		0			0
$274$	−257.845	−	165.707i	−0.941039	−	0.604769i
$275$			53.1896i			0.193417i
$276$		0			0
$277$	−240.875			−0.869586			−0.434793	−	0.900530i	$-0.643178\pi$
$277$	−240.875			−0.869586			−0.434793	+	0.900530i	$0.643178\pi$
$278$	155.207	−	241.507i	0.558300	−	0.868731i
$279$		0			0
$280$	−93.8012	−	205.396i	−0.335004	−	0.733557i
$281$	55.9740	−	190.630i	0.199196	−	0.678399i	−0.797938	−	0.602740i	$-0.794076\pi$
$281$	55.9740	−	190.630i	0.199196	−	0.678399i	0.997134	−	0.0756590i	$-0.0241060\pi$
$282$		0			0
$283$	−88.3756	+	101.991i	−0.312281	+	0.360392i	−0.890094	−	0.455778i	$-0.849361\pi$
$283$	−88.3756	+	101.991i	−0.312281	+	0.360392i	0.577812	+	0.816170i	$0.303907\pi$
$284$	202.925	+	29.1762i	0.714523	+	0.102733i
$285$		0			0
$286$	−58.2404	−	67.2130i	−0.203638	−	0.235010i
$287$	−102.084	−	158.845i	−0.355692	−	0.553468i
$288$		0			0
$289$	43.8130	+	50.5629i	0.151602	+	0.174958i
$290$	71.4836	+	243.451i	0.246495	+	0.839486i
$291$		0			0
$292$	0.806729	−	0.931014i	0.00276277	−	0.00318841i
$293$	−290.553	−	132.691i	−0.991648	−	0.452870i	−0.147547	−	0.989055i	$-0.547138\pi$
$293$	−290.553	−	132.691i	−0.991648	−	0.452870i	−0.844101	+	0.536185i	$0.819865\pi$
$294$		0			0
$295$	−141.372	−	309.561i	−0.479227	−	1.04936i
$296$	−130.231	+	18.7244i	−0.439970	+	0.0632582i
$297$		0			0
$298$	124.919			0.419190
$299$	−484.965	−	280.782i	−1.62196	−	0.939069i
$300$		0			0
$301$	35.8330	+	23.0284i	0.119046	+	0.0765064i
$302$	355.644	−	51.1339i	1.17763	−	0.169317i
$303$		0			0
$304$	−47.1101	−	13.8328i	−0.154967	−	0.0455025i
$305$	19.1152	+	8.72964i	0.0626729	+	0.0286218i
$306$		0			0
$307$	−15.6683	+	108.975i	−0.0510367	+	0.354968i	0.948261	+	0.317492i	$0.102841\pi$
$307$	−15.6683	+	108.975i	−0.0510367	+	0.354968i	−0.999298	+	0.0374757i	$0.988068\pi$
$308$	−17.1923	−	58.5515i	−0.0558191	−	0.190102i
$309$		0			0
$310$	−291.110	+	187.085i	−0.939066	+	0.603501i
$311$	−122.581	−	190.740i	−0.394152	−	0.613313i	0.586294	−	0.810098i	$-0.300586\pi$
$311$	−122.581	−	190.740i	−0.394152	−	0.613313i	−0.980447	+	0.196785i	$0.936950\pi$
$312$		0			0
$313$	43.4557	−	12.7598i	0.138836	−	0.0407660i	−0.211576	−	0.977362i	$-0.567860\pi$
$313$	43.4557	−	12.7598i	0.138836	−	0.0407660i	0.350412	+	0.936596i	$0.386041\pi$
$314$	−163.257	−	23.4728i	−0.519926	−	0.0747541i
$315$		0			0
$316$	−113.446	+	248.411i	−0.359005	+	0.786112i
$317$	−54.0899	+	184.213i	−0.170631	+	0.581114i	0.829126	+	0.559061i	$0.188838\pi$
$317$	−54.0899	+	184.213i	−0.170631	+	0.581114i	−0.999757	+	0.0220528i	$0.992980\pi$
$318$		0			0
$319$	9.75865	+	67.8729i	0.0305914	+	0.212768i
$320$	−29.2090	+	45.4501i	−0.0912781	+	0.142032i
$321$		0			0
$322$	−222.656	−	313.482i	−0.691478	−	0.973548i
$323$			231.568i			0.716929i
$324$		0			0
$325$	71.4548	+	496.979i	0.219861	+	1.52917i
$326$	133.921	−	61.1597i	0.410801	−	0.187606i
$327$		0			0
$328$	−18.7677	+	41.0955i	−0.0572186	+	0.125291i
$329$	708.351	+	613.789i	2.15304	+	1.86562i
$330$		0			0
$331$	513.135	−	150.670i	1.55026	−	0.455196i	0.609078	−	0.793110i	$-0.291539\pi$
$331$	513.135	−	150.670i	1.55026	−	0.455196i	0.941177	+	0.337914i	$0.109721\pi$
$332$	−45.1552	+	39.1272i	−0.136010	+	0.117853i
$333$		0			0
$334$	−2.95191	+	1.89708i	−0.00883806	+	0.00567988i
$335$	361.746	−	313.454i	1.07984	−	0.935685i
$336$		0			0
$337$	−35.8224	+	249.150i	−0.106298	+	0.739318i	0.865055	+	0.501677i	$0.167283\pi$
$337$	−35.8224	+	249.150i	−0.106298	+	0.739318i	−0.971353	+	0.237641i	$0.923626\pi$
$338$	−453.839	−	393.254i	−1.34272	−	1.16347i
$339$		0			0
$340$	244.487	+	71.7879i	0.719080	+	0.211141i
$341$	−85.0681	+	38.8493i	−0.249466	+	0.113928i
$342$		0			0
$343$	415.109	+	266.774i	1.21023	+	0.777768i
$344$		−	10.1915i		−	0.0296264i
$345$		0			0
$346$	−31.6379			−0.0914389
$347$	82.1344	−	127.804i	0.236698	−	0.368310i	−0.702501	−	0.711683i	$-0.747933\pi$
$347$	82.1344	−	127.804i	0.236698	−	0.368310i	0.939199	+	0.343373i	$0.111570\pi$
$348$		0			0
$349$	63.8389	+	139.788i	0.182920	+	0.400538i	0.978772	−	0.204953i	$-0.0657041\pi$
$349$	63.8389	+	139.788i	0.182920	+	0.400538i	−0.795852	+	0.605491i	$0.792977\pi$
$350$	−97.0598	+	330.555i	−0.277314	+	0.944444i
$351$		0			0
$352$	−9.56152	+	11.0346i	−0.0271634	+	0.0313482i
$353$	408.145	+	58.6824i	1.15622	+	0.166239i	0.693628	−	0.720333i	$-0.256011\pi$
$353$	408.145	+	58.6824i	1.15622	+	0.166239i	0.462590	+	0.886572i	$0.346920\pi$
$354$		0			0
$355$	−453.330	−	523.171i	−1.27699	−	1.47372i
$356$	152.816	+	237.786i	0.429258	+	0.667939i
$357$		0			0
$358$	−7.29333	−	8.41695i	−0.0203724	−	0.0235110i
$359$	−81.0080	−	275.888i	−0.225649	−	0.768490i	−0.992019	−	0.126090i	$-0.959757\pi$
$359$	−81.0080	−	275.888i	−0.225649	−	0.768490i	0.766370	−	0.642400i	$-0.222061\pi$
$360$		0			0
$361$	137.737	−	158.957i	0.381544	−	0.440325i
$362$	16.4726	+	7.52280i	0.0455045	+	0.0207812i
$363$		0			0
$364$	−239.295	−	523.982i	−0.657403	−	1.43951i
$365$	−4.11740	+	0.591993i	−0.0112806	+	0.00162190i
$366$		0			0
$367$	156.483			0.426383			0.213192	−	0.977010i	$-0.431614\pi$
$367$	156.483			0.426383			0.213192	+	0.977010i	$0.431614\pi$
$368$	−34.2968	+	85.3682i	−0.0931978	+	0.231979i
$369$		0			0
$370$	373.743	+	240.190i	1.01012	+	0.649162i
$371$	−769.832	+	110.685i	−2.07502	+	0.298343i
$372$		0			0
$373$	−496.117	−	145.673i	−1.33007	−	0.390545i	−0.461955	−	0.886903i	$-0.652852\pi$
$373$	−496.117	−	145.673i	−1.33007	−	0.390545i	−0.868117	+	0.496359i	$0.834670\pi$
$374$	62.6398	+	28.6066i	0.167486	+	0.0764883i
$375$		0			0
$376$	31.9155	−	221.977i	0.0848818	−	0.590366i
$377$	182.361	+	621.063i	0.483715	+	1.64738i
$378$		0			0
$379$	135.588	−	87.1370i	0.357751	−	0.229913i	−0.349402	−	0.936973i	$-0.613615\pi$
$379$	135.588	−	87.1370i	0.357751	−	0.229913i	0.707154	+	0.707060i	$0.249979\pi$
$380$	89.6332	+	139.472i	0.235877	+	0.367032i
$381$		0			0
$382$	45.3160	−	13.3060i	0.118628	−	0.0348324i
$383$	−36.4286	−	5.23764i	−0.0951137	−	0.0136753i	0.0945936	−	0.995516i	$-0.469845\pi$
$383$	−36.4286	−	5.23764i	−0.0951137	−	0.0136753i	−0.189707	+	0.981841i	$0.560754\pi$
$384$		0			0
$385$	−85.5985	+	187.435i	−0.222334	+	0.486843i
$386$	−69.9216	+	238.131i	−0.181144	+	0.616920i
$387$		0			0
$388$	−48.2663	−	335.699i	−0.124398	−	0.865204i
$389$	228.536	−	355.609i	0.587496	−	0.914161i	−0.412499	−	0.910958i	$-0.635344\pi$
$389$	228.536	−	355.609i	0.587496	−	0.914161i	0.999995	−	0.00320307i	$-0.00101957\pi$
$390$		0			0
$391$	431.890	+	41.7705i	1.10458	+	0.106830i
$392$		−	256.657i		−	0.654737i
$393$		0			0
$394$	5.33261	+	37.0891i	0.0135346	+	0.0941349i
$395$	838.801	−	383.068i	2.12355	−	0.969792i
$396$		0			0
$397$	90.9337	−	199.117i	0.229052	−	0.501554i	−0.759854	−	0.650093i	$-0.774730\pi$
$397$	90.9337	−	199.117i	0.229052	−	0.501554i	0.988907	+	0.148539i	$0.0474571\pi$
$398$	−52.1126	−	45.1559i	−0.130936	−	0.113457i
$399$		0			0
$400$	79.0908	−	23.2231i	0.197727	−	0.0580579i
$401$	−274.287	+	237.671i	−0.684009	+	0.592697i	−0.925974	−	0.377588i	$-0.876754\pi$
$401$	−274.287	+	237.671i	−0.684009	+	0.592697i	0.241965	+	0.970285i	$0.422208\pi$
$402$		0			0
$403$	−742.647	+	477.270i	−1.84280	+	1.18429i
$404$	45.1160	−	39.0932i	0.111673	−	0.0967653i
$405$		0			0
$406$	−63.2070	+	439.614i	−0.155682	+	1.08279i
$407$	90.7390	+	78.6258i	0.222946	+	0.193184i
$408$		0			0
$409$	−613.916	−	180.262i	−1.50102	−	0.440738i	−0.574979	−	0.818168i	$-0.694990\pi$
$409$	−613.916	−	180.262i	−1.50102	−	0.440738i	−0.926038	+	0.377430i	$0.876808\pi$
$410$	138.766	−	63.3722i	0.338453	−	0.154566i
$411$		0			0
$412$	94.5857	+	60.7865i	0.229577	+	0.147540i
$413$		−	595.698i		−	1.44237i
$414$		0			0
$415$	201.752			0.486150
$416$	−74.5146	+	115.947i	−0.179122	+	0.278719i
$417$		0			0
$418$	18.6128	+	40.7564i	0.0445283	+	0.0975034i
$419$	−78.2230	+	266.403i	−0.186690	+	0.635807i	0.811953	+	0.583723i	$0.198405\pi$
$419$	−78.2230	+	266.403i	−0.186690	+	0.635807i	−0.998643	+	0.0520841i	$0.983414\pi$
$420$		0			0
$421$	−525.911	+	606.933i	−1.24919	+	1.44165i	−0.397505	+	0.917600i	$0.630124\pi$
$421$	−525.911	+	606.933i	−1.24919	+	1.44165i	−0.851689	+	0.524047i	$0.824422\pi$
$422$	−432.723	−	62.2162i	−1.02541	−	0.147432i
$423$		0			0
$424$	121.862	+	140.637i	0.287411	+	0.331690i
$425$	−210.184	−	327.053i	−0.494550	−	0.769535i
$426$		0			0
$427$	24.0884	+	27.7995i	0.0564132	+	0.0651043i
$428$	−7.17924	−	24.4502i	−0.0167739	−	0.0571267i
$429$		0			0
$430$	−22.5359	+	26.0078i	−0.0524090	+	0.0604832i
$431$	−133.179	−	60.8209i	−0.309001	−	0.141116i	0.254879	−	0.966973i	$-0.417964\pi$
$431$	−133.179	−	60.8209i	−0.309001	−	0.141116i	−0.563879	+	0.825857i	$0.690692\pi$
$432$		0			0
$433$	−17.0209	−	37.2706i	−0.0393093	−	0.0860753i	0.888959	−	0.457987i	$-0.151430\pi$
$433$	−17.0209	−	37.2706i	−0.0393093	−	0.0860753i	−0.928268	+	0.371912i	$0.878702\pi$
$434$	−599.561	+	86.2038i	−1.38148	+	0.198626i
$435$		0			0
$436$	179.658			0.412059
$437$	194.574	+	204.561i	0.445249	+	0.468102i
$438$		0			0
$439$	−270.086	−	173.574i	−0.615230	−	0.395384i	0.195585	−	0.980687i	$-0.437339\pi$
$439$	−270.086	−	173.574i	−0.615230	−	0.395384i	−0.810815	+	0.585303i	$0.800976\pi$
$440$	48.8003	−	7.01643i	0.110910	−	0.0159464i
$441$		0			0
$442$	623.707	+	183.137i	1.41110	+	0.414337i
$443$	−68.0622	−	31.0829i	−0.153639	−	0.0701647i	0.337111	−	0.941465i	$-0.390550\pi$
$443$	−68.0622	−	31.0829i	−0.153639	−	0.0701647i	−0.490751	+	0.871300i	$0.663277\pi$
$444$		0			0
$445$	135.831	−	944.723i	0.305237	−	2.12297i
$446$	40.4377	+	137.718i	0.0906675	+	0.308785i
$447$		0			0
$448$	−79.5573	+	51.1284i	−0.177583	+	0.114126i
$449$	301.243	+	468.743i	0.670919	+	1.04397i	0.995186	+	0.0980046i	$0.0312460\pi$
$449$	301.243	+	468.743i	0.670919	+	1.04397i	−0.324267	+	0.945966i	$0.605118\pi$
$450$		0			0
$451$	39.5575	−	11.6151i	0.0877106	−	0.0257542i
$452$	138.071	+	19.8515i	0.305466	+	0.0439193i
$453$		0			0
$454$	83.9740	−	183.877i	0.184965	−	0.405016i
$455$	−547.994	+	1866.30i	−1.20438	+	4.10175i
$456$		0			0
$457$	−43.6023	−	303.260i	−0.0954098	−	0.663590i	−0.980260	−	0.197714i	$-0.936648\pi$
$457$	−43.6023	−	303.260i	−0.0954098	−	0.663590i	0.884850	−	0.465876i	$-0.154261\pi$
$458$	295.391	−	459.638i	0.644959	−	1.00358i
$459$		0			0
$460$	276.292	−	142.014i	0.600636	−	0.308725i
$461$			646.978i			1.40342i	0.712461	+	0.701712i	$0.247581\pi$
$461$			646.978i			1.40342i	−0.712461	+	0.701712i	$0.752419\pi$
$462$		0			0
$463$	95.3539	+	663.201i	0.205948	+	1.43240i	0.786205	+	0.617966i	$0.212043\pi$
$463$	95.3539	+	663.201i	0.205948	+	1.43240i	−0.580257	+	0.814433i	$0.697048\pi$
$464$	96.6634	−	44.1447i	0.208326	−	0.0951395i
$465$		0			0
$466$	−238.402	+	522.028i	−0.511593	+	1.12023i
$467$	−545.660	−	472.817i	−1.16844	−	1.01246i	−0.999641	−	0.0268049i	$-0.991467\pi$
$467$	−545.660	−	472.817i	−1.16844	−	1.01246i	−0.168796	−	0.985651i	$-0.553988\pi$
$468$		0			0
$469$	803.920	−	236.052i	1.71411	−	0.503309i
$470$	−572.292	+	495.894i	−1.21764	+	1.05509i
$471$		0			0
$472$	−119.904	+	77.0578i	−0.254035	+	0.163258i
$473$	−7.02867	+	6.09038i	−0.0148598	+	0.0128761i
$474$		0			0
$475$	35.9987	−	250.376i	0.0757867	−	0.527108i
$476$	337.084	+	292.085i	0.708159	+	0.613623i
$477$		0			0
$478$	109.825	+	32.2474i	0.229759	+	0.0674632i
$479$	−106.456	+	48.6166i	−0.222245	+	0.101496i	−0.523426	−	0.852071i	$-0.675346\pi$
$479$	−106.456	+	48.6166i	−0.222245	+	0.101496i	0.301181	+	0.953567i	$0.402619\pi$
$480$		0			0
$481$	953.449	+	612.744i	1.98222	+	1.27390i
$482$		−	366.475i		−	0.760321i
$483$		0			0
$484$	−228.676			−0.472471
$485$	−619.142	+	963.403i	−1.27658	+	1.98640i
$486$		0			0
$487$	195.527	+	428.145i	0.401494	+	0.879148i	0.997117	+	0.0758843i	$0.0241780\pi$
$487$	195.527	+	428.145i	0.401494	+	0.879148i	−0.595623	+	0.803264i	$0.703095\pi$
$488$	2.47958	−	8.44467i	0.00508111	−	0.0173047i
$489$		0			0
$490$	−567.531	+	654.966i	−1.15823	+	1.33666i
$491$	−421.318	−	60.5764i	−0.858082	−	0.123374i	−0.300790	−	0.953690i	$-0.597250\pi$
$491$	−421.318	−	60.5764i	−0.858082	−	0.123374i	−0.557292	+	0.830317i	$0.688160\pi$
$492$		0			0
$493$	−328.210	−	378.775i	−0.665741	−	0.768306i
$494$	228.662	+	355.805i	0.462878	+	0.720252i
$495$		0			0
$496$	94.9089	+	109.531i	0.191349	+	0.220828i
$497$	−341.388	−	1162.66i	−0.686897	−	2.33936i
$498$		0			0
$499$	165.717	−	191.248i	0.332098	−	0.383262i	−0.565002	−	0.825090i	$-0.691124\pi$
$499$	165.717	−	191.248i	0.332098	−	0.383262i	0.897100	+	0.441828i	$0.145670\pi$
$500$	53.9674	+	24.6461i	0.107935	+	0.0492922i
$501$		0			0
$502$	202.246	+	442.858i	0.402881	+	0.882187i
$503$	−416.854	+	59.9345i	−0.828735	+	0.119154i	−0.543612	−	0.839337i	$-0.682944\pi$
$503$	−416.854	+	59.9345i	−0.828735	+	0.119154i	−0.285123	+	0.958491i	$0.592035\pi$
$504$		0			0
$505$	−201.577			−0.399162
$506$	79.3707	−	27.3624i	0.156859	−	0.0540760i
$507$		0			0
$508$	−205.278	−	131.924i	−0.404091	−	0.259694i
$509$	−207.447	+	29.8263i	−0.407557	+	0.0585979i	−0.343045	−	0.939319i	$-0.611458\pi$
$509$	−207.447	+	29.8263i	−0.407557	+	0.0585979i	−0.0645124	+	0.997917i	$0.520549\pi$
$510$		0			0
$511$	−6.98640	−	2.05139i	−0.0136720	−	0.00401447i
$512$	20.5826	+	9.39977i	0.0402004	+	0.0183589i
$513$		0			0
$514$	82.1246	−	571.189i	0.159776	−	1.11126i
$515$	−106.960	−	364.274i	−0.207690	−	0.707328i
$516$		0			0
$517$	−172.162	+	110.642i	−0.333002	+	0.214007i
$518$	420.436	+	654.212i	0.811653	+	1.26296i
$519$		0			0
$520$	446.542	−	131.116i	0.858734	−	0.252147i
$521$	18.4825	+	2.65738i	0.0354750	+	0.00510054i	0.160030	−	0.987112i	$-0.448841\pi$
$521$	18.4825	+	2.65738i	0.0354750	+	0.00510054i	−0.124554	+	0.992213i	$0.539750\pi$
$522$		0			0
$523$	−74.0594	+	162.168i	−0.141605	+	0.310072i	−0.967125	−	0.254301i	$-0.918155\pi$
$523$	−74.0594	+	162.168i	−0.141605	+	0.310072i	0.825520	+	0.564373i	$0.190882\pi$
$524$	4.90594	−	16.7081i	0.00936249	−	0.0318857i
$525$		0			0
$526$	34.4863	+	239.858i	0.0655634	+	0.456003i
$527$	369.550	−	575.031i	0.701234	−	1.09114i
$528$		0			0
$529$	416.616	−	325.994i	0.787554	−	0.616245i
$530$		−	628.360i		−	1.18559i
$531$		0			0
$532$	41.3005	+	287.252i	0.0776326	+	0.539947i
$533$	354.003	−	161.668i	0.664171	−	0.303317i
$534$		0			0
$535$	−35.7447	+	78.2699i	−0.0668125	+	0.146299i
$536$	−151.506	−	131.281i	−0.282661	−	0.244927i
$537$		0			0
$538$	−56.5040	+	16.5911i	−0.105026	+	0.0308384i
$539$	−177.006	+	153.377i	−0.328397	+	0.284558i
$540$		0			0
$541$	447.711	−	287.726i	0.827562	−	0.531842i	−0.0569402	−	0.998378i	$-0.518134\pi$
$541$	447.711	−	287.726i	0.827562	−	0.531842i	0.884502	+	0.466536i	$0.154498\pi$
$542$	386.104	−	334.561i	0.712368	−	0.617271i
$543$		0			0
$544$	15.1877	−	105.633i	0.0279186	−	0.194178i
$545$	−458.471	−	397.267i	−0.841231	−	0.728931i
$546$		0			0
$547$	213.747	+	62.7616i	0.390761	+	0.114738i	0.471210	−	0.882021i	$-0.343817\pi$
$547$	213.747	+	62.7616i	0.390761	+	0.114738i	−0.0804490	+	0.996759i	$0.525635\pi$
$548$	394.286	−	180.065i	0.719501	−	0.328585i
$549$		0			0
$550$	−63.2803	−	40.6678i	−0.115055	−	0.0739415i
$551$		−	326.099i		−	0.591830i
$552$		0			0
$553$	1614.13			2.91886
$554$	184.169	−	286.572i	0.332435	−	0.517278i
$555$		0			0
$556$	168.656	+	369.304i	0.303337	+	0.664216i
$557$	−166.060	+	565.548i	−0.298133	+	1.01535i	0.665117	+	0.746739i	$0.268382\pi$
$557$	−166.060	+	565.548i	−0.298133	+	1.01535i	−0.963250	+	0.268607i	$0.913437\pi$
$558$		0			0
$559$	−57.4909	+	66.3480i	−0.102846	+	0.118690i
$560$	316.081	+	45.4455i	0.564430	+	0.0811528i
$561$		0			0
$562$	183.998	+	212.345i	0.327399	+	0.377838i
$563$	263.079	+	409.359i	0.467281	+	0.727104i	0.992282	−	0.123998i	$-0.0395716\pi$
$563$	263.079	+	409.359i	0.467281	+	0.727104i	−0.525001	+	0.851101i	$0.675935\pi$
$564$		0			0
$565$	−308.447	−	355.967i	−0.545924	−	0.630030i
$566$	−53.7695	−	183.122i	−0.0949990	−	0.323537i
$567$		0			0
$568$	−189.864	+	219.114i	−0.334267	+	0.385765i
$569$	544.396	+	248.617i	0.956759	+	0.436937i	0.831708	−	0.555213i	$-0.187363\pi$
$569$	544.396	+	248.617i	0.956759	+	0.436937i	0.125051	+	0.992150i	$0.460091\pi$
$570$		0			0
$571$	−6.24388	−	13.6722i	−0.0109350	−	0.0239443i	0.904086	−	0.427351i	$-0.140553\pi$
$571$	−6.24388	−	13.6722i	−0.0109350	−	0.0239443i	−0.915021	+	0.403407i	$0.867826\pi$
$572$	124.494	−	17.8995i	0.217646	−	0.0312928i
$573$		0			0
$574$	267.031			0.465211
$575$	−460.474	−	112.303i	−0.800825	−	0.195309i
$576$		0			0
$577$	−279.044	−	179.331i	−0.483611	−	0.310798i	0.276020	−	0.961152i	$-0.410984\pi$
$577$	−279.044	−	179.331i	−0.483611	−	0.310798i	−0.759632	+	0.650354i	$0.774621\pi$
$578$	−93.6540	+	13.4654i	−0.162031	+	0.0232966i
$579$		0			0
$580$	−344.291	−	101.093i	−0.593606	−	0.174298i
$581$	321.240	+	146.705i	0.552908	+	0.252505i
$582$		0			0
$583$	24.1673	−	168.088i	0.0414534	−	0.288315i
$584$	0.490829	+	1.67161i	0.000840461	+	0.00286235i
$585$		0			0
$586$	380.015	−	244.221i	0.648491	−	0.416760i
$587$	152.124	+	236.710i	0.259155	+	0.403254i	0.946312	−	0.323256i	$-0.104778\pi$
$587$	152.124	+	236.710i	0.259155	+	0.403254i	−0.687156	+	0.726510i	$0.741141\pi$
$588$		0			0
$589$	426.729	−	125.299i	0.724497	−	0.212732i
$590$	476.379	+	68.4930i	0.807422	+	0.116090i
$591$		0			0
$592$	77.2957	−	169.254i	0.130567	−	0.285902i
$593$	273.298	−	930.766i	0.460873	−	1.56959i	−0.321582	−	0.946882i	$-0.604215\pi$
$593$	273.298	−	930.766i	0.460873	−	1.56959i	0.782455	−	0.622707i	$-0.213967\pi$
$594$		0			0
$595$	−214.337	−	1490.75i	−0.360231	−	2.50546i
$596$	−95.5104	+	148.617i	−0.160252	+	0.249358i
$597$		0			0
$598$	704.845	−	362.288i	1.17867	−	0.605834i
$599$			1084.33i			1.81023i	0.425163	+	0.905117i	$0.360217\pi$
$599$			1084.33i			1.81023i	−0.425163	+	0.905117i	$0.639783\pi$
$600$		0			0
$601$	113.207	+	787.370i	0.188364	+	1.31010i	0.836244	+	0.548357i	$0.184747\pi$
$601$	113.207	+	787.370i	0.188364	+	1.31010i	−0.647880	+	0.761742i	$0.724344\pi$
$602$	−54.7944	+	25.0238i	−0.0910207	+	0.0415677i
$603$		0			0
$604$	−211.084	+	462.210i	−0.349477	+	0.765248i
$605$	583.561	+	505.658i	0.964564	+	0.835799i
$606$		0			0
$607$	102.403	−	30.0682i	0.168703	−	0.0495357i	−0.196290	−	0.980546i	$-0.562889\pi$
$607$	102.403	−	30.0682i	0.168703	−	0.0495357i	0.364993	+	0.931010i	$0.381071\pi$
$608$	52.4765	−	45.4712i	0.0863101	−	0.0747881i
$609$		0			0
$610$	−25.0009	+	16.0671i	−0.0409851	+	0.0263395i
$611$	−1459.96	+	1265.07i	−2.38947	+	2.07049i
$612$		0			0
$613$	−82.8421	+	576.179i	−0.135142	+	0.939934i	0.803565	+	0.595217i	$0.202934\pi$
$613$	−82.8421	+	576.179i	−0.135142	+	0.939934i	−0.938707	+	0.344717i	$0.887975\pi$
$614$	−117.669	−	101.961i	−0.191644	−	0.166060i
$615$		0			0
$616$	82.8043	+	24.3135i	0.134423	+	0.0394700i
$617$	−263.016	+	120.115i	−0.426282	+	0.194677i	−0.616991	−	0.786970i	$-0.711649\pi$
$617$	−263.016	+	120.115i	−0.426282	+	0.194677i	0.190709	+	0.981647i	$0.438921\pi$
$618$		0			0
$619$	−802.141	−	515.505i	−1.29587	−	0.832802i	−0.303111	−	0.952955i	$-0.598025\pi$
$619$	−802.141	−	515.505i	−1.29587	−	0.832802i	−0.992755	+	0.120153i	$0.961662\pi$
$620$		−	489.380i		−	0.789322i
$621$		0			0
$622$	320.650			0.515514
$623$	903.237	−	1405.46i	1.44982	−	2.25596i
$624$		0			0
$625$	−297.238	−	650.859i	−0.475580	−	1.04138i
$626$	−18.0450	+	61.4557i	−0.0288259	+	0.0981720i
$627$		0			0
$628$	152.749	−	176.282i	0.243231	−	0.280703i
$629$	−868.633	−	124.891i	−1.38098	−	0.198554i
$630$		0			0
$631$	−254.531	−	293.745i	−0.403378	−	0.465523i	0.517324	−	0.855790i	$-0.326928\pi$
$631$	−254.531	−	293.745i	−0.403378	−	0.465523i	−0.920702	+	0.390267i	$0.872383\pi$
$632$	−208.799	−	324.898i	−0.330379	−	0.514080i
$633$		0			0
$634$	−177.805	−	205.197i	−0.280449	−	0.323655i
$635$	232.135	+	790.581i	0.365568	+	1.24501i
$636$		0			0
$637$	−1447.82	+	1670.87i	−2.27287	+	2.62303i
$638$	−88.2105	−	40.2844i	−0.138261	−	0.0631417i
$639$		0			0
$640$	−31.7399	−	69.5006i	−0.0495935	−	0.108595i
$641$	−426.469	+	61.3170i	−0.665319	+	0.0956584i	−0.466696	−	0.884418i	$-0.654556\pi$
$641$	−426.469	+	61.3170i	−0.665319	+	0.0956584i	−0.198623	+	0.980076i	$0.563647\pi$
$642$		0			0
$643$	317.314			0.493490			0.246745	−	0.969080i	$-0.420639\pi$
$643$	317.314			0.493490			0.246745	+	0.969080i	$0.420639\pi$
$644$	543.193	−	25.2134i	0.843467	−	0.0391513i
$645$		0			0
$646$	−275.499	−	177.053i	−0.426470	−	0.274075i
$647$	328.012	−	47.1610i	0.506974	−	0.0728918i	0.115918	−	0.993259i	$-0.463019\pi$
$647$	328.012	−	47.1610i	0.506974	−	0.0728918i	0.391056	+	0.920367i	$0.372110\pi$
$648$		0			0
$649$	124.798	+	36.6440i	0.192293	+	0.0564622i
$650$	−645.895	−	294.971i	−0.993685	−	0.453801i
$651$		0			0
$652$	−29.6311	+	206.089i	−0.0454465	+	0.316088i
$653$	187.341	+	638.024i	0.286892	+	0.977065i	0.969256	+	0.246053i	$0.0791337\pi$
$653$	187.341	+	638.024i	0.286892	+	0.977065i	−0.682364	+	0.731012i	$0.739048\pi$
$654$		0			0
$655$	−49.4653	+	31.7894i	−0.0755195	+	0.0485334i
$656$	−34.5424	−	53.7491i	−0.0526561	−	0.0819345i
$657$		0			0
$658$	−1271.82	+	373.441i	−1.93286	+	0.567540i
$659$	440.547	+	63.3410i	0.668508	+	0.0961169i	0.468209	−	0.883618i	$-0.344900\pi$
$659$	440.547	+	63.3410i	0.668508	+	0.0961169i	0.200299	+	0.979735i	$0.435809\pi$
$660$		0			0
$661$	−356.750	+	781.173i	−0.539712	+	1.18180i	0.421711	+	0.906730i	$0.361430\pi$
$661$	−356.750	+	781.173i	−0.539712	+	1.18180i	−0.961423	+	0.275074i	$0.911298\pi$
$662$	−213.079	+	725.682i	−0.321872	+	1.09620i
$663$		0			0
$664$	−12.0253	−	83.6377i	−0.0181104	−	0.125960i
$665$	529.788	−	824.366i	0.796674	−	1.23965i
$666$		0			0
$667$	−608.195	−	58.8220i	−0.911836	−	0.0881889i
$668$		−	4.96240i		−	0.00742874i
$669$		0			0
$670$	96.3364	+	670.035i	0.143786	+	1.00005i
$671$	−7.30575	+	3.33642i	−0.0108879	+	0.00497232i
$672$		0			0
$673$	531.985	−	1164.88i	0.790467	−	1.73088i	0.115158	−	0.993347i	$-0.463262\pi$
$673$	531.985	−	1164.88i	0.790467	−	1.73088i	0.675309	−	0.737535i	$-0.264010\pi$
$674$	−269.028	−	233.114i	−0.399151	−	0.345867i
$675$		0			0
$676$	814.856	−	239.263i	1.20541	−	0.353940i
$677$	−787.832	+	682.660i	−1.16371	+	1.00836i	−0.163950	+	0.986469i	$0.552424\pi$
$677$	−787.832	+	682.660i	−1.16371	+	1.00836i	−0.999760	+	0.0218924i	$0.993031\pi$
$678$		0			0
$679$	−1686.37	+	1083.77i	−2.48361	+	1.59612i
$680$	−272.337	+	235.982i	−0.400496	+	0.347032i
$681$		0			0
$682$	18.8220	−	130.910i	0.0275983	−	0.191950i
$683$	112.099	+	97.1342i	0.164127	+	0.142217i	0.733052	−	0.680172i	$-0.238095\pi$
$683$	112.099	+	97.1342i	0.164127	+	0.142217i	−0.568925	+	0.822389i	$0.692641\pi$
$684$		0			0
$685$	−1404.35	−	412.355i	−2.05015	−	0.601978i
$686$	−634.769	+	289.889i	−0.925320	+	0.422579i
$687$		0			0
$688$	12.1249	+	7.79222i	0.0176234	+	0.0113259i
$689$		−	1603.00i		−	2.32656i
$690$		0			0
$691$	−202.656			−0.293279			−0.146639	−	0.989190i	$-0.546846\pi$
$691$	−202.656			−0.293279			−0.146639	+	0.989190i	$0.546846\pi$
$692$	24.1897	−	37.6399i	0.0349562	−	0.0543930i
$693$		0			0
$694$	89.2510	+	195.433i	0.128604	+	0.281603i
$695$	386.228	−	1315.37i	0.555723	−	1.89262i
$696$		0			0
$697$	−197.333	+	227.734i	−0.283118	+	0.326735i
$698$	−215.117	−	30.9292i	−0.308191	−	0.0443112i
$699$		0			0
$700$	−319.055	−	368.210i	−0.455794	−	0.526014i
$701$	−299.347	−	465.793i	−0.427029	−	0.664469i	0.559355	−	0.828928i	$-0.311049\pi$
$701$	−299.347	−	465.793i	−0.427029	−	0.664469i	−0.986384	+	0.164459i	$0.947412\pi$
$702$		0			0
$703$	−373.916	−	431.522i	−0.531886	−	0.613830i
$704$	−5.81741	−	19.8123i	−0.00826337	−	0.0281425i
$705$		0			0
$706$	−381.875	+	440.708i	−0.540900	+	0.624232i
$707$	−320.960	−	146.578i	−0.453975	−	0.207323i
$708$		0			0
$709$	103.353	+	226.312i	0.145773	+	0.319199i	0.968408	−	0.249372i	$-0.0802240\pi$
$709$	103.353	+	226.312i	0.145773	+	0.319199i	−0.822635	+	0.568570i	$0.807497\pi$
$710$	969.031	−	139.326i	1.36483	−	0.196233i
$711$		0			0
$712$	−399.737			−0.561429
$713$	−156.717	−	818.478i	−0.219799	−	1.14794i
$714$		0			0
$715$	−357.277	−	229.608i	−0.499688	−	0.321130i
$716$	15.5901	−	2.24152i	0.0217739	−	0.00313061i
$717$		0			0
$718$	390.165	+	114.563i	0.543405	+	0.159558i
$719$	1034.62	+	472.496i	1.43897	+	0.657157i	0.973663	−	0.227990i	$-0.0732154\pi$
$719$	1034.62	+	472.496i	1.43897	+	0.657157i	0.465311	+	0.885148i	$0.345943\pi$
$720$		0			0
$721$	94.5762	−	657.792i	0.131174	−	0.912333i
$722$	83.8021	+	285.404i	0.116069	+	0.395296i
$723$		0			0
$724$	−21.5447	+	13.8459i	−0.0297578	+	0.0191242i
$725$	295.985	+	460.561i	0.408255	+	0.635257i
$726$		0			0
$727$	1171.05	−	343.851i	1.61080	−	0.472973i	0.652274	−	0.757984i	$-0.273815\pi$
$727$	1171.05	−	343.851i	1.61080	−	0.472973i	0.958524	+	0.285011i	$0.0919971\pi$
$728$	806.348	+	115.935i	1.10762	+	0.159252i
$729$		0			0
$730$	2.44379	−	5.35115i	0.00334765	−	0.00733034i
$731$	19.1512	−	65.2230i	0.0261986	−	0.0892244i
$732$		0			0
$733$	−112.591	−	783.085i	−0.153603	−	1.06833i	−0.910117	−	0.414352i	$-0.864008\pi$
$733$	−112.591	−	783.085i	−0.153603	−	1.06833i	0.756514	−	0.653977i	$-0.226901\pi$
$734$	−119.644	+	186.169i	−0.163002	+	0.253637i
$735$		0			0
$736$	−75.3409	−	106.074i	−0.102365	−	0.144123i
$737$			182.941i			0.248224i
$738$		0			0
$739$	156.219	+	1086.52i	0.211392	+	1.47026i	0.768515	+	0.639832i	$0.220996\pi$
$739$	156.219	+	1086.52i	0.211392	+	1.47026i	−0.557123	+	0.830430i	$0.688095\pi$
$740$	−571.514	+	261.002i	−0.772316	+	0.352705i
$741$		0			0
$742$	456.916	−	1000.51i	0.615790	−	1.34839i
$743$	−850.931	−	737.336i	−1.14526	−	0.992377i	−0.999996	−	0.00298450i	$-0.999050\pi$
$743$	−850.931	−	737.336i	−1.14526	−	0.992377i	−0.145268	−	0.989392i	$-0.546405\pi$
$744$		0			0
$745$	572.363	−	168.061i	0.768272	−	0.225585i
$746$	552.631	−	478.857i	0.740792	−	0.641900i
$747$		0			0
$748$	−81.9269	+	52.6512i	−0.109528	+	0.0703893i
$749$	−113.829	+	98.6333i	−0.151975	+	0.131687i
$750$		0			0
$751$	38.0101	−	264.366i	0.0506127	−	0.352019i	−0.948740	−	0.316056i	$-0.897641\pi$
$751$	38.0101	−	264.366i	0.0506127	−	0.352019i	0.999353	−	0.0359627i	$-0.0114498\pi$
$752$	239.687	+	207.690i	0.318733	+	0.276184i
$753$		0			0
$754$	−878.316	−	257.897i	−1.16488	−	0.342038i
$755$	1560.73	−	712.760i	2.06719	−	0.944053i
$756$		0			0
$757$	−331.202	−	212.850i	−0.437519	−	0.281176i	0.303282	−	0.952901i	$-0.401917\pi$
$757$	−331.202	−	212.850i	−0.437519	−	0.281176i	−0.740801	+	0.671725i	$0.765554\pi$
$758$			227.934i			0.300704i
$759$		0			0
$760$	−234.463			−0.308504
$761$	120.836	−	188.025i	0.158786	−	0.247076i	−0.752740	−	0.658318i	$-0.771268\pi$
$761$	120.836	−	188.025i	0.158786	−	0.247076i	0.911526	+	0.411241i	$0.134905\pi$
$762$		0			0
$763$	−441.125	−	965.929i	−0.578145	−	1.26596i
$764$	−18.8175	+	64.0865i	−0.0246302	+	0.0838828i
$765$		0			0
$766$	34.0839	−	39.3349i	0.0444959	−	0.0513510i
$767$	1215.28	+	174.731i	1.58446	+	0.227811i
$768$		0			0
$769$	282.593	+	326.130i	0.367481	+	0.424096i	0.909132	−	0.416508i	$-0.136746\pi$
$769$	282.593	+	326.130i	0.367481	+	0.424096i	−0.541651	+	0.840603i	$0.682201\pi$
$770$	−157.546	−	245.147i	−0.204605	−	0.318372i
$771$		0			0
$772$	−229.847	−	265.257i	−0.297729	−	0.343597i
$773$	108.577	+	369.778i	0.140461	+	0.478367i	0.999434	−	0.0336548i	$-0.0107147\pi$
$773$	108.577	+	369.778i	0.140461	+	0.478367i	−0.858972	+	0.512022i	$0.828897\pi$
$774$		0			0
$775$	−488.957	+	564.287i	−0.630913	+	0.728112i
$776$	436.289	+	199.246i	0.562228	+	0.256761i
$777$		0			0
$778$	248.338	+	543.784i	0.319200	+	0.698951i
$779$	−194.068	+	27.9027i	−0.249124	+	0.0358186i
$780$		0			0
$781$	264.576			0.338766
$782$	−379.910	+	481.887i	−0.485818	+	0.616224i
$783$		0			0
$784$	305.348	+	196.235i	0.389474	+	0.250300i
$785$	−779.604	+	112.090i	−0.993126	+	0.142790i
$786$		0			0
$787$	1132.28	+	332.467i	1.43873	+	0.422448i	0.905797	−	0.423712i	$-0.139273\pi$
$787$	1132.28	+	332.467i	1.43873	+	0.422448i	0.532929	+	0.846160i	$0.321091\pi$
$788$	−48.2026	−	22.0134i	−0.0611708	−	0.0279358i
$789$		0			0
$790$	−185.592	+	1290.82i	−0.234926	+	1.63395i
$791$	−232.281	−	791.078i	−0.293655	−	1.00010i
$792$		0			0
$793$	−63.7794	+	40.9885i	−0.0804280	+	0.0516879i
$794$	167.366	+	260.426i	0.210788	+	0.327993i
$795$		0			0
$796$	93.5668	−	27.4737i	0.117546	−	0.0345147i
$797$	1305.24	+	187.665i	1.63769	+	0.235464i	0.898799	−	0.438362i	$-0.144441\pi$
$797$	1305.24	+	187.665i	1.63769	+	0.235464i	0.738890	+	0.673826i	$0.235350\pi$
$798$		0			0
$799$	621.378	−	1360.63i	0.777695	−	1.70291i
$800$	−32.8425	+	111.851i	−0.0410531	+	0.139814i
$801$		0			0
$802$	−73.0455	−	508.042i	−0.0910791	−	0.633469i
$803$	0.859528	−	1.33745i	0.00107040	−	0.00166557i
$804$		0			0
$805$	−1441.93	−	1136.79i	−1.79122	−	1.41216i
$806$		−	1248.45i		−	1.54894i
$807$		0			0
$808$	12.0148	+	83.5649i	0.0148698	+	0.103422i
$809$	−129.775	+	59.2663i	−0.160414	+	0.0732587i	−0.494004	−	0.869460i	$-0.664467\pi$
$809$	−129.775	+	59.2663i	−0.160414	+	0.0732587i	0.333590	+	0.942718i	$0.391740\pi$
$810$		0			0
$811$	340.546	−	745.692i	0.419909	−	0.919473i	−0.574949	−	0.818190i	$-0.694978\pi$
$811$	340.546	−	745.692i	0.419909	−	0.919473i	0.994858	−	0.101283i	$-0.0322948\pi$
$812$	−474.687	−	411.319i	−0.584590	−	0.506551i
$813$		0			0
$814$	−162.919	+	47.8374i	−0.200147	+	0.0587684i
$815$	531.330	−	460.400i	0.651938	−	0.564908i
$816$		0			0
$817$	37.2076	−	23.9119i	0.0455417	−	0.0292679i
$818$	683.849	−	592.558i	0.836001	−	0.724399i
$819$		0			0
$820$	−30.7031	+	213.545i	−0.0374428	+	0.260420i
$821$	1188.87	+	1030.16i	1.44808	+	1.25477i	0.911741	+	0.410765i	$0.134738\pi$
$821$	1188.87	+	1030.16i	1.44808	+	1.25477i	0.536338	+	0.844003i	$0.319807\pi$
$822$		0			0
$823$	405.529	+	119.074i	0.492745	+	0.144683i	0.518659	−	0.854981i	$-0.326431\pi$
$823$	405.529	+	119.074i	0.492745	+	0.144683i	−0.0259142	+	0.999664i	$0.508250\pi$
$824$	−144.637	+	66.0535i	−0.175530	+	0.0801620i
$825$		0			0
$826$	708.709	+	455.460i	0.858001	+	0.551404i
$827$		−	743.481i		−	0.899009i	−0.893278	−	0.449505i	$-0.851601\pi$
$827$		−	743.481i		−	0.899009i	0.893278	−	0.449505i	$-0.148399\pi$
$828$		0			0
$829$	204.499			0.246681			0.123341	−	0.992364i	$-0.460639\pi$
$829$	204.499			0.246681			0.123341	+	0.992364i	$0.460639\pi$
$830$	−154.256	+	240.027i	−0.185851	+	0.289189i
$831$		0			0
$832$	−80.9710	−	177.302i	−0.0973209	−	0.213103i
$833$	482.294	−	1642.54i	0.578984	−	1.97184i
$834$		0			0
$835$	−10.9731	+	12.6636i	−0.0131414	+	0.0151660i
$836$	−62.7194	−	9.01769i	−0.0750232	−	0.0107867i
$837$		0			0
$838$	−257.135	−	296.750i	−0.306844	−	0.354117i
$839$	414.268	+	644.614i	0.493764	+	0.768312i	0.995302	−	0.0968238i	$-0.0308683\pi$
$839$	414.268	+	644.614i	0.493764	+	0.768312i	−0.501537	+	0.865136i	$0.667232\pi$
$840$		0			0
$841$	−88.5462	−	102.188i	−0.105287	−	0.121507i
$842$	−319.974	−	1089.73i	−0.380017	−	1.29422i
$843$		0			0
$844$	404.872	−	467.247i	0.479706	−	0.553610i
$845$	−2608.51	−	1191.27i	−3.08700	−	1.40978i
$846$		0			0
$847$	561.482	+	1229.47i	0.662907	+	1.45156i
$848$	−260.491	+	37.4530i	−0.307183	+	0.0441662i
$849$		0			0
$850$	549.801			0.646825
$851$	−872.264	+	619.539i	−1.02499	+	0.728013i
$852$		0			0
$853$	514.895	+	330.903i	0.603628	+	0.387928i	0.806463	−	0.591285i	$-0.201379\pi$
$853$	514.895	+	330.903i	0.603628	+	0.387928i	−0.202835	+	0.979213i	$0.565015\pi$
$854$	−51.4910	+	7.40329i	−0.0602939	+	0.00866895i
$855$		0			0
$856$	34.5779	+	10.1530i	0.0403947	+	0.0118610i
$857$	−1237.48	−	565.140i	−1.44397	−	0.659440i	−0.469291	−	0.883044i	$-0.655490\pi$
$857$	−1237.48	−	565.140i	−1.44397	−	0.659440i	−0.974680	+	0.223604i	$0.928218\pi$
$858$		0			0
$859$	−234.463	+	1630.73i	−0.272949	+	1.89840i	0.144171	+	0.989553i	$0.453948\pi$
$859$	−234.463	+	1630.73i	−0.272949	+	1.89840i	−0.417120	+	0.908851i	$0.636961\pi$
$860$	−13.7113	−	46.6963i	−0.0159433	−	0.0542980i
$861$		0			0
$862$	174.186	−	111.942i	0.202072	−	0.129864i
$863$	917.140	+	1427.10i	1.06273	+	1.65365i	0.686514	+	0.727117i	$0.259140\pi$
$863$	917.140	+	1427.10i	1.06273	+	1.65365i	0.376220	+	0.926530i	$0.377224\pi$
$864$		0			0
$865$	−144.961	+	42.5644i	−0.167585	+	0.0492074i
$866$	57.3552	+	8.24643i	0.0662300	+	0.00952244i
$867$		0			0
$868$	355.855	−	779.214i	0.409972	−	0.897712i
$869$	−99.2923	+	338.158i	−0.114260	+	0.389135i
$870$		0			0
$871$	245.762	+	1709.31i	0.282161	+	1.96247i
$872$	−137.363	+	213.741i	−0.157526	+	0.245116i
$873$		0			0
$874$	−392.136	+	75.0835i	−0.448668	+	0.0859079i
$875$		−	350.670i		−	0.400766i
$876$		0			0
$877$	−213.219	−	1482.97i	−0.243123	−	1.69096i	−0.636259	−	0.771475i	$-0.719519\pi$
$877$	−213.219	−	1482.97i	−0.243123	−	1.69096i	0.393137	−	0.919480i	$-0.371390\pi$
$878$	413.005	−	188.613i	0.470393	−	0.214821i
$879$		0			0
$880$	−28.9643	+	63.4230i	−0.0329140	+	0.0720715i
$881$	−911.751	−	790.037i	−1.03490	−	0.896750i	−0.0401659	−	0.999193i	$-0.512789\pi$
$881$	−911.751	−	790.037i	−1.03490	−	0.896750i	−0.994739	+	0.102443i	$0.967334\pi$
$882$		0			0
$883$	−119.197	+	34.9993i	−0.134990	+	0.0396368i	−0.348530	−	0.937298i	$-0.613319\pi$
$883$	−119.197	+	34.9993i	−0.134990	+	0.0396368i	0.213539	+	0.976934i	$0.431501\pi$
$884$	−694.755	+	602.009i	−0.785922	+	0.681006i
$885$		0			0
$886$	89.0188	−	57.2089i	0.100473	−	0.0645699i
$887$	−1060.70	+	919.102i	−1.19583	+	1.03619i	−0.197390	+	0.980325i	$0.563247\pi$
$887$	−1060.70	+	919.102i	−1.19583	+	1.03619i	−0.998438	+	0.0558663i	$0.982208\pi$
$888$		0			0
$889$	−205.258	+	1427.60i	−0.230886	+	1.60585i
$890$	1020.09	+	883.917i	1.14617	+	0.993165i
$891$		0			0
$892$	−194.763	−	57.1876i	−0.218344	−	0.0641116i
$893$	885.289	−	404.298i	0.991365	−	0.452741i
$894$		0			0
$895$	−44.7411	−	28.7533i	−0.0499900	−	0.0321266i
$896$		−	133.742i		−	0.149266i
$897$		0			0
$898$	−787.993			−0.877498
$899$	−520.407	+	809.770i	−0.578873	+	0.900745i
$900$		0			0
$901$	515.614	+	1129.04i	0.572269	+	1.25309i
$902$	−16.4263	+	55.9427i	−0.0182109	+	0.0620208i
$903$		0			0
$904$	−129.184	+	149.086i	−0.142902	+	0.164918i
$905$	85.5968	+	12.3070i	0.0945820	+	0.0135988i
$906$		0			0
$907$	85.7957	+	99.0135i	0.0945929	+	0.109166i	0.801072	−	0.598568i	$-0.204263\pi$
$907$	85.7957	+	99.0135i	0.0945929	+	0.109166i	−0.706479	+	0.707734i	$0.749718\pi$
$908$	154.556	+	240.494i	0.170216	+	0.264861i
$909$		0			0
$910$	−1801.37	−	2078.89i	−1.97953	−	2.28449i
$911$	295.223	+	1005.44i	0.324064	+	1.10366i	0.946959	+	0.321356i	$0.104138\pi$
$911$	295.223	+	1005.44i	0.324064	+	1.10366i	−0.622894	+	0.782306i	$0.714043\pi$
$912$		0			0
$913$	−50.4954	+	58.2748i	−0.0553072	+	0.0638279i
$914$	394.130	+	179.993i	0.431215	+	0.196929i
$915$		0			0
$916$	320.986	+	702.861i	0.350421	+	0.767315i
$917$	−101.877	+	14.6477i	−0.111098	+	0.0159735i
$918$		0			0
$919$	1235.85			1.34478			0.672389	−	0.740198i	$-0.265268\pi$
$919$	1235.85			1.34478			0.672389	+	0.740198i	$0.265268\pi$
$920$	−42.2927	+	437.289i	−0.0459704	+	0.475315i
$921$		0			0
$922$	−769.718	−	494.668i	−0.834835	−	0.536516i
$923$	2472.08	−	355.431i	2.67831	−	0.385083i
$924$		0			0
$925$	919.769	+	270.069i	0.994345	+	0.291966i
$926$	−861.924	−	393.628i	−0.930803	−	0.425084i
$927$		0			0
$928$	−21.3876	+	148.754i	−0.0230470	+	0.160295i
$929$	167.180	+	569.363i	0.179957	+	0.612877i	0.999221	+	0.0394607i	$0.0125640\pi$
$929$	167.180	+	569.363i	0.179957	+	0.612877i	−0.819264	+	0.573416i	$0.805618\pi$
$930$		0			0
$931$	937.016	−	602.183i	1.00646	−	0.646814i
$932$	−438.785	−	682.763i	−0.470799	−	0.732578i
$933$		0			0
$934$	979.718	−	287.671i	1.04895	−	0.307999i
$935$	325.495	+	46.7991i	0.348123	+	0.0500525i
$936$		0			0
$937$	−534.327	+	1170.01i	−0.570253	+	1.24868i	0.376410	+	0.926453i	$0.377158\pi$
$937$	−534.327	+	1170.01i	−0.570253	+	1.24868i	−0.946663	+	0.322226i	$0.895569\pi$
$938$	−333.828	+	1136.91i	−0.355893	+	1.21206i
$939$		0			0
$940$	−152.407	−	1060.01i	−0.162135	−	1.12767i
$941$	−852.394	+	1326.35i	−0.905838	+	1.40951i	0.00645768	+	0.999979i	$0.497944\pi$
$941$	−852.394	+	1326.35i	−0.905838	+	1.40951i	−0.912296	+	0.409532i	$0.865692\pi$
$942$		0			0
$943$	17.0342	+	366.982i	0.0180639	+	0.389164i
$944$		−	201.569i		−	0.213526i
$945$		0			0
$946$	−1.87180	−	13.0187i	−0.00197865	−	0.0137618i
$947$	645.532	−	294.805i	0.681660	−	0.311304i	−0.0443219	−	0.999017i	$-0.514113\pi$
$947$	645.532	−	294.805i	0.681660	−	0.311304i	0.725982	+	0.687713i	$0.241385\pi$
$948$		0			0
$949$	6.23431	−	13.6512i	0.00656934	−	0.0143849i
$950$	270.352	+	234.261i	0.284581	+	0.246591i
$951$		0			0
$952$	−605.225	+	177.710i	−0.635740	+	0.186670i
$953$	−232.035	+	201.060i	−0.243479	+	0.210975i	−0.768048	−	0.640392i	$-0.778772\pi$
$953$	−232.035	+	201.060i	−0.243479	+	0.210975i	0.524569	+	0.851368i	$0.324226\pi$
$954$		0			0
$955$	189.731	−	121.933i	0.198672	−	0.127679i
$956$	−122.335	+	106.004i	−0.127965	+	0.110883i
$957$		0			0
$958$	23.5542	−	163.823i	0.0245868	−	0.171005i
$959$	−1936.23	−	1677.75i	−2.01901	−	1.74948i
$960$		0			0
$961$	−337.542	−	99.1112i	−0.351240	−	0.103133i
$962$	−1457.98	+	665.837i	−1.51557	+	0.692138i
$963$		0			0
$964$	435.999	+	280.200i	0.452281	+	0.290664i
$965$			1185.16i			1.22814i
$966$		0			0
$967$	−330.476			−0.341754			−0.170877	−	0.985292i	$-0.554660\pi$
$967$	−330.476			−0.341754			−0.170877	+	0.985292i	$0.554660\pi$
$968$	174.841	−	272.059i	0.180621	−	0.281052i
$969$		0			0
$970$	−672.788	−	1473.20i	−0.693596	−	1.51876i
$971$	247.172	−	841.789i	0.254554	−	0.866930i	−0.728722	−	0.684809i	$-0.759886\pi$
$971$	247.172	−	841.789i	0.254554	−	0.866930i	0.983276	−	0.182121i	$-0.0582963\pi$
$972$		0			0
$973$	1571.45	−	1813.55i	1.61506	−	1.86387i
$974$	−658.866	−	94.7307i	−0.676454	−	0.0972594i
$975$		0			0
$976$	8.15089	+	9.40663i	0.00835132	+	0.00963794i
$977$	372.880	+	580.213i	0.381659	+	0.593872i	0.977936	−	0.208906i	$-0.0669904\pi$
$977$	372.880	+	580.213i	0.381659	+	0.593872i	−0.596277	+	0.802779i	$0.703354\pi$
$978$		0			0
$979$	238.881	+	275.683i	0.244005	+	0.281597i
$980$	−345.297	−	1175.97i	−0.352344	−	1.19997i
$981$		0			0
$982$	394.201	−	454.932i	0.401427	−	0.463271i
$983$	1025.01	+	468.107i	1.04274	+	0.476203i	0.861777	−	0.507288i	$-0.169352\pi$
$983$	1025.01	+	468.107i	1.04274	+	0.476203i	0.180962	+	0.983490i	$0.442079\pi$
$984$		0			0
$985$	74.3319	+	162.764i	0.0754638	+	0.165243i
$986$	701.577	−	100.871i	0.711538	−	0.102304i
$987$		0			0
$988$	−598.136			−0.605400
$989$	−37.8856	−	73.7078i	−0.0383070	−	0.0745276i
$990$		0			0
$991$	−481.780	−	309.621i	−0.486155	−	0.312433i	0.274502	−	0.961586i	$-0.411487\pi$
$991$	−481.780	−	309.621i	−0.486155	−	0.312433i	−0.760657	+	0.649153i	$0.775123\pi$
$992$	−202.876	+	29.1691i	−0.204512	+	0.0294043i
$993$		0			0
$994$	1644.25	+	482.796i	1.65418	+	0.485710i
$995$	−299.525	−	136.789i	−0.301031	−	0.137476i
$996$		0			0
$997$	141.087	−	981.283i	0.141512	−	0.984235i	−0.788061	−	0.615597i	$-0.788915\pi$
$997$	141.087	−	981.283i	0.141512	−	0.984235i	0.929573	−	0.368638i	$-0.120176\pi$
$998$	100.825	+	343.380i	0.101027	+	0.344068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.3.k.a.71.1	yes	80
3.2	odd	2	inner	414.3.k.a.71.8	yes	80
23.12	even	11	inner	414.3.k.a.35.8	yes	80
69.35	odd	22	inner	414.3.k.a.35.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.a.35.1	✓	80	69.35	odd	22	inner
414.3.k.a.35.8	yes	80	23.12	even	11	inner
414.3.k.a.71.1	yes	80	1.1	even	1	trivial
414.3.k.a.71.8	yes	80	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	414.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-1.90263 + 6.47977i) q^{5} +(-7.74127 + 8.93390i) q^{7} +(2.79964 + 0.402527i) q^{8} +O(q^{10})\)	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-1.90263 + 6.47977i) q^{5} +(-7.74127 + 8.93390i) q^{7} +(2.79964 + 0.402527i) q^{8} +(-6.25434 - 7.21790i) q^{10} +(-1.39544 - 2.17135i) q^{11} +(-15.9554 - 18.4135i) q^{13} +(-4.70994 - 16.0406i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(17.1606 + 7.83698i) q^{17} +(5.09911 + 11.1655i) q^{19} +(13.3692 - 1.92220i) q^{20} +3.65021 q^{22} +(21.7442 - 7.49613i) q^{23} +(-17.3361 - 11.1412i) q^{25} +(34.1059 - 4.90369i) q^{26} +(22.6848 + 6.66086i) q^{28} +(-24.1659 - 11.0362i) q^{29} +(5.15642 - 35.8637i) q^{31} +(-1.59372 - 5.42771i) q^{32} +(-22.4444 + 14.4242i) q^{34} +(-43.1608 - 67.1596i) q^{35} +(-44.6329 + 13.1054i) q^{37} +(-17.1824 - 2.47046i) q^{38} +(-7.93497 + 17.3751i) q^{40} +(-4.50009 + 15.3259i) q^{41} +(-0.512794 - 3.56656i) q^{43} +(-2.79088 + 4.34270i) q^{44} +(-7.70694 + 31.6007i) q^{46} -79.2879i q^{47} +(-12.9139 - 89.8183i) q^{49} +(26.5097 - 12.1066i) q^{50} +(-20.2428 + 44.3254i) q^{52} +(49.7226 + 43.0849i) q^{53} +(16.7249 - 4.91086i) q^{55} +(-25.2689 + 21.8956i) q^{56} +(31.6067 - 20.3124i) q^{58} +(-38.0838 + 32.9998i) q^{59} +(0.442839 - 3.08002i) q^{61} +(38.7249 + 33.5554i) q^{62} +(7.67594 + 2.25386i) q^{64} +(149.672 - 68.3530i) q^{65} +(-59.6258 - 38.3192i) q^{67} -37.7309i q^{68} +112.901 q^{70} +(-55.4188 + 86.2333i) q^{71} +(0.255877 + 0.560292i) q^{73} +(18.5338 - 63.1204i) q^{74} +(16.0765 - 18.5533i) q^{76} +(30.2011 + 4.34227i) q^{77} +(-89.4179 - 103.194i) q^{79} +(-14.6045 - 22.7250i) q^{80} +(-14.7927 - 17.0717i) q^{82} +(-8.41661 - 28.6644i) q^{83} +(-83.4322 + 96.2858i) q^{85} +(4.63525 + 2.11685i) q^{86} +(-3.03270 - 6.64070i) q^{88} +(-139.890 + 20.1131i) q^{89} +288.019 q^{91} +(-31.7031 - 33.3303i) q^{92} +(94.3298 + 60.6221i) q^{94} +(-82.0516 + 11.7972i) q^{95} +(162.707 + 47.7750i) q^{97} +(116.732 + 53.3095i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^4 - 16 * q^7	\( 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) \) 80 * q + 16 * q^4 - 16 * q^7 + 8 * q^10 + 8 * q^13 - 32 * q^16 - 128 * q^19 - 32 * q^22 - 352 * q^25 + 32 * q^28 + 32 * q^31 - 300 * q^34 - 384 * q^37 - 16 * q^40 + 540 * q^43 - 80 * q^49 - 16 * q^52 + 1244 * q^55 + 424 * q^58 + 568 * q^61 + 64 * q^64 + 60 * q^67 + 296 * q^70 + 36 * q^73 - 96 * q^76 - 1476 * q^79 + 12 * q^82 - 276 * q^85 - 112 * q^88 - 368 * q^91 - 304 * q^94 + 712 * q^97

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